function [a,b] = powerlaw(x,y,x_name,y_name,plt)
%Plot basic power law fits on a log log plot from linear data
% Input values as x and y, and (optional) x_name & y_name (strings) as the 
% x and y axis names.
%
% Karlie Rees
% University of Utah
% 

if ~exist('x_name','var') || ischar(x_name) == 0   
    x_name = 'x';           % If x_name and y_name are not defined, 
end                         % or if they are not char, just default 
                            % them to x and y

if ~exist('y_name','var') || ischar(y_name) == 0 
    y_name = 'y';
end

if ~exist('plt','var') 
    plt = 1;
end


log_x = log(x);         % Convert x and y data into logs
log_y = log(y);

fit = polyfit(log_x,log_y,1);   % Find linear fit of log data
c1 = exp(fit(2));               % Coefficient

[p,S] = polyfit(log_x,log_y,1);
[y_fit,delta] = polyval(p,log_x,S);
R2 = 1 - (S.normr/norm(log_y - mean(log_y)))^2;

if plt
figure;
loglog(x,y,'o','Color',[0 0.45 0.74],'LineWidth',1); % plot x and y data as circles
hold on
p1 = loglog(x,exp(polyval(fit,log_x)),'-k','LineWidth',2); % plot fit curve
xlabel(x_name,'FontSize',12,'FontWeight','bold');
ylabel(y_name,'FontSize',12,'FontWeight','bold');
legend([p1],sprintf('Fit: %s = %.2f %s^{%.2f} \n    R^2= %.2f',y_name,c1,x_name,fit(1),R2),...
    'FontSize',12,'Location','best');
pbaspect([1 1 1]);
yticks = get(gca,'YTick');
set(gca,'YTickLabel',yticks);
xticks = get(gca,'XTick');
set(gca,'XTickLabel',xticks);
end

a=c1;
b=(fit(1));